vereinfachen ln(2)+1/2 ln(x+1)-2ln(1+sqrt(x))

Lösung

vereinfachen

ln (2) + \frac{1}{2} ln (x + 1) - 2 ln (1 + x)

ln (\frac{2 ( x + 1 ) ^{\frac{1}{2}}}{( 1 + x ) ^{2}})

Schritte zur Lösung

ln (2) + \frac{1}{2} ln (x + 1) - 2 ln (1 + x)

Wende die log Regel an:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (x + 1) = ln ((x + 1)^{\frac{1}{2}})

= ln (2) + ln ((x + 1)^{\frac{1}{2}}) - 2 ln (x + 1)

Wende die log Regel an:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (2) + ln ((x + 1)^{\frac{1}{2}}) = ln (2 (x + 1)^{\frac{1}{2}})

= ln (2 (x + 1)^{\frac{1}{2}}) - 2 ln (1 + x)

Wende die log Regel an:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x + 1) = ln ((x + 1)^{2})

= ln (2 (x + 1)^{\frac{1}{2}}) - ln ((x + 1)^{2})

Wende die log Regel an:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (2 (x + 1)^{\frac{1}{2}}) - ln ((1 + x)^{2}) = ln (\frac{2 ( x + 1 ) ^{\frac{1}{2}}}{( x + 1 ) ^{2}})

= ln (\frac{2 ( x + 1 ) ^{\frac{1}{2}}}{( 1 + x ) ^{2}})

s im pl i f y ln (z) - ln (4 y)

s im pl i f y lo g_{2} (\frac{x}{4})

s im pl i f y \frac{1}{3} lo g_{b} (x) + 4 lo g_{b} (y) - 5 lo g_{b} (x)

s im pl i f y lo g_{3} (x) - lo g_{3} (x^{5})

e x p an d lo g_{10} (\frac{x}{10000})